Hostname: page-component-8448b6f56d-tj2md Total loading time: 0 Render date: 2024-04-24T23:00:45.800Z Has data issue: false hasContentIssue false
  • English
  • Français

On the universality of local dissipation scales in turbulent channel flow

Published online by Cambridge University Press:  01 December 2015

S. C. C. Bailey  and
B. M. Witte
S. C. C. Bailey*
Affiliation:
Department of Mechanical Engineering, University of Kentucky, Lexington, KY 40506, USA
B. M. Witte
Affiliation:
Department of Mechanical Engineering, University of Kentucky, Lexington, KY 40506, USA
*
†Email address for correspondence: sean.bailey@uky.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Well-resolved measurements of the small-scale dissipation statistics within turbulent channel flow are reported for a range of Reynolds numbers from $Re_{{\it\tau}}\approx 500$ to 4000. In this flow, the local large-scale Reynolds number based on the longitudinal integral length scale is found to poorly describe the Reynolds number dependence of the small-scale statistics. When a length scale based on Townsend’s attached-eddy hypothesis is used to define the local large-scale Reynolds number, the Reynolds number scaling behaviour was found to be more consistent with that observed in homogeneous, isotropic turbulence. The Reynolds number scaling of the dissipation moments up to the sixth moment was examined and the results were found to be in good agreement with predicted scaling behaviour (Schumacher et al., Proc. Natl Acad. Sci. USA, vol. 111, 2014, pp. 10961–10965). The probability density functions of the local dissipation scales (Yakhot, Physica D, vol. 215 (2), 2006, pp. 166–174) were also determined and, when the revised local large-scale Reynolds number is used for normalization, provide support for the existence of a universal distribution which scales differently for inner and outer regions.

JFM classification

Turbulent Flows: Turbulence theory Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 786 , 10 January 2016 , pp. 234 - 252
Check for updates
Copyright
© 2015 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

del Álamo, J. C. & Jiménez, J. 2009 Estimation fo turbulent convection velocities and corrections to Taylor’s approximation. J. Fluid Mech. 640, 5–26.CrossRefGoogle Scholar
Anselmet, F., Gagne, Y., Hopfinger, E. J. & Antonia, R. A. 1984 High-order velocity structure functions in turbulent shear flow. J. Fluid Mech. 140, 63–89.CrossRefGoogle Scholar
Bailey, S. C. C., Hultmark, M., Schumacher, J., Yakhot, V. & Smits, A. J. 2009 Measurements of the dissipation scales in turbulent pipe flow. Phys. Rev. Lett. 103, 014502.CrossRefGoogle ScholarPubMed
Bailey, S. C. C., Kunkel, G. J., Hultmark, M., Vallikivi, M., Hill, J. P., Meyer, K. A., Tsay, C., Arnold, C. B. & Smits, A. J. 2010 Turbulence measurements using a nanoscale thermal anemometry probe. J. Fluid Mech. 663, 160–179.CrossRefGoogle Scholar
Bailey, S. C. C. & Smits, A. J. 2010 Experimental investigation of the structure of large- and very-large-scale motions in turbulent pipe flow. J. Fluid Mech. 651, 339–356.CrossRefGoogle Scholar
Bailey, S. C. C., Vallikivi, M., Hultmark, M. & Smits, A. 2014 Estimating the value of von Kármán’s constant in turbulent pipe flow. J. Fluid Mech. 749, 79–98.CrossRefGoogle Scholar
Balakumar, B. J. & Adrian, R. J. 2007 Large- and very-large-scale motions in channel and boundary-layer flows. Phil. Trans. R. Soc. Lond. A 365, 665–681.Google ScholarPubMed
Batchelor, G. K. & Townsend, A. A. 1949 The nature of turbulent motion at large wave-numbers. Proc. R. Soc. Lond. A 199, 238–255.Google Scholar
Biferale, L. 2008 A note on the fluctuation of dissipative scale in turbulence. Phys. Fluids 20, 031703.CrossRefGoogle Scholar
Frisch, U. 1995 Turbulence: The Legacy of A. N. Kolmogorov. Cambridge University Press.CrossRefGoogle Scholar
Frisch, U. & Vergassola, M. 1991 A prediction of the multifractal model: the intermediate dissipation range. Europhys. Lett. 14, 439–444.CrossRefGoogle Scholar
Grant, H. L., Stewart, R. W. & Moilliet, A. 1962 Turbulence spectra from a tidal channel. J. Fluid Mech. 12, 241–268.CrossRefGoogle Scholar
Guala, M., Hommema, S. E. & Adrian, R. J. 2006 Large-scale and very-large-scale motions in turbulent pipe flow. J. Fluid Mech. 554, 521–542.CrossRefGoogle Scholar
Hamlington, P. E., Krasnov, D., Boeck, T. & Schumacher, J. 2012 Local dissipation scales and energy dissipation-rate moments in channel flow. J. Fluid Mech. 701, 419–429.CrossRefGoogle Scholar
Head, M. R. & Bandyopadhyay, P. 1981 New aspects of turbulent boundary-layer structure. J. Fluid Mech. 107, 297–337.CrossRefGoogle Scholar
Hultmark, M., Vallikivi, M., Bailey, S. C. C. & Smits, A. J. 2012 Turbulent pipe flow at extreme Reynolds numbers. Phys. Rev. Lett. 108, 094501.CrossRefGoogle ScholarPubMed
Hultmark, M., Vallikivi, M., Bailey, S. C. C. & Smits, A. J. 2013 Logarithmic scaling of turbulence in smooth- and rough-wall pipe flow. J. Fluid Mech. 728, 376–395.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007 Large-scale influences in near-wall turbulence. Phil. Trans. R. Soc. Lond. A 365, 647–664.Google ScholarPubMed
Hutchins, N., Nickels, T. B., Marusic, I. & Chong, M. S. 2009 Hot-wire spatial resolution issues in wall-bounded turbulence. J. Fluid Mech. 635, 103–136.CrossRefGoogle Scholar
Kim, K. C. & Adrian, R. J. 1999 Very large-scale motion in the outer layer. Phys. Fluids 11 (2), 417–422.CrossRefGoogle Scholar
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30, 741–773.CrossRefGoogle Scholar
Kolmogorov, A. N. 1941 The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk SSSR 30, 301–305.Google Scholar
Marusic, I., McKeon, B. J., Monkewitz, P. A., Nagib, H. M., Smits, A. J. & Sreenivasan, K. R. 2010 Wall-bounded turbulent flows at high Reynolds numbers: recent advances and key issues. Phys. Fluids 22, 065103.CrossRefGoogle Scholar
Mathis, R., Hutchins, N. & Marusic, I. 2009 Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers. J. Fluid Mech. 628, 311–337.CrossRefGoogle Scholar
Meneveau, C. & Sreenivasan, K. R. 1991 The multifractal nature of turbulent energy dissipation. J. Fluid Mech. 224, 429–484.CrossRefGoogle Scholar
Monty, J. P.2005 Developments in smooth wall turbulent duct flows. PhD thesis, University of Melbourne.Google Scholar
Monty, J. P., Hutchins, N., Ng, H. C. H., Marusic, I. & Chong, M. S. 2009 A comparison of turbulent pipe, channel and boundary layer flows. J. Fluid Mech. 632, 431–442.CrossRefGoogle Scholar
Monty, J. P., Stewart, J. A., Williams, R. C. & Chong, M. S. 2007 Large-scale features in turbulent pipe and channel flows. J. Fluid Mech. 589, 147–156.CrossRefGoogle Scholar
Morrison, J. F., McKeon, B. J., Jiang, W. & Smits, A. J. 2004 Scaling of the streamwise velocity component in turbulent pipe flow. J. Fluid Mech. 508, 99–131.CrossRefGoogle Scholar
Morshed, N. M., Venayagamoorthy, S. K. & Dasi, L. P. 2013 Intermittency and local dissipation scales under strong mean shear. Phys. Fluids 25, 011701.CrossRefGoogle Scholar
Nelkin, M. 1990 Multifractal scaling of velocity derivatives in turbulence. Phys. Rev. A 42 (12), 7226–7229.CrossRefGoogle ScholarPubMed
Paladin, G. & Vulpiani, A. 1987 Degrees of freedom of turbulence. Phys. Rev. A 35, 1971–1973.CrossRefGoogle ScholarPubMed
Perry, A. E., Henbest, S. & Chong, M. S. 1986 A theoretical and experimental study of wall turbulence. J. Fluid Mech. 165, 163–199.CrossRefGoogle Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Saddoughi, S. G. & Veeravalli, S. V. 1994 Local isotropy in turbulent boundary layers at high Reynolds number. J. Fluid Mech. 268, 333–372.CrossRefGoogle Scholar
Saddoughi, S. G. & Veeravalli, S. V. 1996 Hot-wire anemometry behaviour at very high frequencies. Meas. Sci. Technol. 7, 1297–1300.CrossRefGoogle Scholar
Schumacher, J. 2007 Sub-Kolmogorov-scale fluctuations in fluid turbulence. Europhys. Lett. 80, 54001,1–6.CrossRefGoogle Scholar
Schumacher, J., Scheel, J. D., Krasnov, D., Donzis, D. A., Yakhot, V. & Sreenivasan, K. R. 2014 Small-scale universality in fluid turbulence. Proc. Natl Acad. Sci. USA 111, 10961–10965.CrossRefGoogle ScholarPubMed
Schumacher, J., Sreenivasan, K. R. & Yakhot, V. 2007 Asymptotic exponents from low-Reynolds-number flows. New J. Phys. 9, 89.CrossRefGoogle Scholar
Tavoularis, S. 2005 Measurement in Fluid Mechanics. Cambridge University Press.Google Scholar
Taylor, G. I. 1938 The spectrum of turbulence. Proc. R. Soc. Lond. A 164 (919), 476–490.CrossRefGoogle Scholar
Tomkins, C. D. & Adrian, R. J. 2005 Energetic spanwise modes in the logarithmic layer of a turbulent boundary layer. J. Fluid Mech. 545, 141–162.CrossRefGoogle Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.Google Scholar
Vallikivi, M., Ganapathisubramani, B. & Smits, A. J. 2015 Spectral scaling in boundary layers and pipes at very high Reynolds numbers. J. Fluid Mech. 771, 303–326.CrossRefGoogle Scholar
Vallikivi, M., Hultmark, M., Bailey, S. C. C. & Smits, A. J. 2011 Turbulence measurements in pipe flow using a nano-scale thermal anemometry probe. Exp. Fluids 51, 1521–1527.CrossRefGoogle Scholar
Vallikivi, M. & Smits, A. J. 2014 Fabrication and characterization of a novel nanoscale thermal anemometry probe. J. Microelectromech. Syst. 23 (4), 899–907.CrossRefGoogle Scholar
Yakhot, V. 2006 Probability densities in strong turbulence. Physica D 215 (2), 166–174.CrossRefGoogle Scholar
Yakhot, V. & Sreenivasan, K. R. 2004 Towards a dynamical theory of multifractals in turbulence. Physica A 343, 147–155.CrossRefGoogle Scholar
Yakhot, V. & Sreenivasan, K. R. 2005 Anomalous scaling of structure functions and dynamic constraints on turbulence simulations. J. Stat. Phys. 121, 823–841.CrossRefGoogle Scholar
Zaman, K. B. M. Q. & Hussain, A. K. M. F. 1981 Taylor hypothesis and large-scale coherent structures. J. Fluid Mech. 112, 379–396.CrossRefGoogle Scholar
Zanoun, E. S., Durst, F. & Nagib, H. 2003 Evaluating the law of the wall in two-dimensional fully developed turbulent channel flows. Phys. Fluids 15, 3079–3089.CrossRefGoogle Scholar
Zhou, Q. & Xia, K.-Q. 2010 Universality of local dissipation scales in buoyancy-driven turbulence. Phys. Rev. Lett. 104, 124301.CrossRefGoogle ScholarPubMed